Image reconstruction from a fiducial collection of scale space interest points and attributes (e.g. in terms of image derivatives) can be used to make the amount of information contained in them explicit. Previous work by various authors includes both linear and non-linear image reconstruction schemes. In this paper, the authors present new results on image reconstruction using a top point repr...

The freezing of the cooperative reorientational motions in orientationally disordered (OD) molecular crystals marks the so-called “glassy” transition, which may be considered a lower-dimensional version of the structural glass transition. While structural glasses display both positional and orientational disorder, in fact, in orientational glasses the disorder involves exclusively the orientati...

The term fractional calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. In a letter to L’Hospital in 1695 Leibniz raised the following question (Miller and Ross...

This work brings together two recently discussed topics: mathematical modeling of a bioreactor and working with derivatives non-integer order. Generally, it turns out that is reasonable to replace the integer order in some already well known models describing bioprocesses fractional ones. However, specific structure such type makes study properties real challenge. contains primary results for a...

Abstract In this article, by virtue of expansions two finite products finitely many square sums, with the aid series composite functions (hyperbolic) sine and cosine inverse functions, in light properties partial Bell polynomials, author establishes Taylor’s real powers containing squares terms Stirling numbers first kind, presents a closed-form formula specific polynomials at sequence derivati...

A dynamical system is a particle or set of particles whose state changes over time. The dynamics the described by differential equations. If derivatives involved are non-integer order, we obtain fractional system. In this paper, considered with Caputo derivative. We collocated problem in dyadic nodes and used refinable functions as approximation to achieve good degree freedom choice regularity....